GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 06 Dec 2019, 14:13

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The symbol ∆ denotes one of the four arithmetic operations:addition,su

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 522
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 22 Jun 2017, 16:18
8
Top Contributor
20
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:06) correct 28% (01:08) wrong based on 1527 sessions

HideShow timer Statistics

The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Most Helpful Expert Reply
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3723
The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post Updated on: 29 Jul 2019, 10:32
5
3
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations: addition,subtraction,multiplication,or division. If 6∆3≤ 3, which of the following must be true ?

I.2∆2=0
II.2∆2=1
III.4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

If 6 ∆ 3 ≤ 3, then the ∆ operator is subtraction AND division.

6 - 3 = 3, which satisfies the equation

\(\frac{6}{3}\) = 2, which also satisfies the equation (2 is less than 3).

The operator cannot be addition or multiplication. 6 + 3 = 9, which is > 3. And 6 * 3 = 18, also > than 3.

Check I, II, and III.

I. 2 ∆ 2 = 0. If ∆ were only subtraction, this would be fine. 2 - 2 = 0.

But \(\frac{2}{2}\) = 1. This equation is not true when ∆ is division. Incorrect.

II. 2 ∆ 2 = 1. If ∆ were only division, this would be fine.\(\frac{2}{2}\) = 1. But when ∆ is subtraction, then 2 - 2 = 0. This equation does not hold true when ∆ is subtraction. Incorrect.

III. 4 ∆ 2 = 2. This must be true for both subtraction and division.

It holds for subtraction. 4 - 4 = 2
And it holds for division: \(\frac{4}{2}\)= 2. Correct.

Answer C
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead

Originally posted by generis on 22 Jun 2017, 17:43.
Last edited by generis on 29 Jul 2019, 10:32, edited 3 times in total.
General Discussion
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 734
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 22 Jun 2017, 17:49
2
1
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I.2∆2=0
I I .2∆2=1
I I I .4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


\(6∆3≤ 3\)

\(\frac{6}{3}= 3\)

\(6-3 = 3\)

Therefore symbol ∆ should be division and subtraction both.

Checking the options, we get;

I.\(2∆2=0\)

\(2 - 2 = 0\)

\(\frac{2}{2}= 1\)------------ Must Not be true.

II .\(2∆2=1\)

\(\frac{2}{2}= 1\)

\(2 - 2 = 0\) --------------- Must Not be true.

III .\(4∆2=2\)

\(\frac{4}{2} = 2\) --------- Must be true.

\(4 - 2 = 2\) --------- Must be true.

Hence Only III must be true. Answer (C)...
Senior Manager
Senior Manager
avatar
G
Joined: 28 May 2017
Posts: 276
Concentration: Finance, General Management
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 23 Jun 2017, 01:59
1
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I.2∆2=0
I I .2∆2=1
I I I .4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

∆ could be either Subtraction or Division in order to fulfill condition 6∆3≤ 3
I - 2∆2=0 - In this condition, ∆ denotes only subtraction and not Division. Hence Wrong
II - 2∆2=1 - In this condition, ∆ denotes only Division and not subtraction. Hence Wrong
III - 4∆2=1 - In this condition, ∆ denotes either Division or subtraction. Hence Correct.

hence, Answer C
Manager
Manager
User avatar
B
Joined: 17 Feb 2016
Posts: 89
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
Reviews Badge
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 23 Jun 2017, 02:24
From the context, \(∆= subtraction and division\)
∆= subtraction\(6-3<=3\)
∆= division\(\frac{6}{3}=2<=3\)

From the options
Only iii holds true as 4∆2=2( both division and subtraction)

Option c
_________________
Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 26 Jun 2017, 18:00
2
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I.2∆2=0
I I .2∆2=1
I I I .4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Let’s analyze the given inequality:

If ∆ = addition:

6 + 3 ≤ 3

9 ≤ 3

Since 9 is not less than 3, ∆ cannot be addition.

If ∆ = subtraction:

6 - 3 ≤ 3

3 ≤ 3

Since 3 is less than or equal to 3, ∆ can be subtraction.

If ∆ = divison:

6/3 ≤ 3

2 ≤ 3

Since 2 is less than or equal to 3, ∆ can be division.

If ∆ = multiplication:

6 x 3 ≤ 3

18 ≤ 3

Since 18 is not less than or equal to 3, ∆ cannot be multiplication.

We see then that ∆ is either subtraction or division. Now let’s analyze each Roman numeral:

I. 2∆2=0

Since 2/2 does not equal 0, division doesn’t work and I is not true.

II. 2∆2=1

Since 2 - 2 does not equal 1, subtraction doesn’t work and II is not true.

III. 4∆2=2

Since 4 - 2 = 2 and 4/2 = 2, III is true.

Answer: C
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4125
Location: Canada
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 27 Jun 2017, 15:49
1
Top Contributor
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2=0
II. 2∆2=1
III. 4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


The above solutions are perfect.
I just want to point out that, when answering this type of question type (where the answer choices are I only, II and III only, etc.), be sure to ELIMINATE answer choices after examining each statement.

So, for example, once we determine that statement I need not be true, we can ELIMINATE answer choices A, D and E
Then, once we determine that statement II need not be true, we can ELIMINATE answer choice B

At this point, there's no need to check statement III, since we already know that the correct answer must be C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
User avatar
B
Joined: 16 Feb 2016
Posts: 22
GMAT ToolKit User
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 10 Jul 2017, 12:43
1
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I.2∆2=0
I I .2∆2=1
I I I .4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III




I read the options as

III (.4)∆2=2

and got it all wrong!!

That dot, right after the Roman Numerals, is so confusing...!
The dot is closer to the digit, rather, it should be closer to the Roman numeral, to avoid any confusion! So I suggest, this question must be edited!

Thanks,
ashygoyal
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59587
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 10 Jul 2017, 12:48
ashygoyal wrote:
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I.2∆2=0
I I .2∆2=1
I I I .4∆2=2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III




I read the options as

III (.4)∆2=2

and got it all wrong!!

That dot, right after the Roman Numerals, is so confusing...!
The dot is closer to the digit, rather, it should be closer to the Roman numeral, to avoid any confusion! So I suggest, this question must be edited!

Thanks,
ashygoyal


Edited as suggested. Thank you.
_________________
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 10 Jul 2017, 23:21
1
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


6∆3≤ 3

So, 6 - 3 = 3
6/3 = 2

I. 2∆2
2-2 = 0
2/2 = 1
So it may be true.

II. 2∆2
2-2 = 0
2/2 = 1
So it is may be true.

III. 4∆2
4-2 = 2
4/2 = 2
So, 4∆2 = 2 must be true.

Answer C.
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2434
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 11 Jul 2017, 01:06
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


6∆3≤ 3
∆ can denote subtraction or division .
6+3=9 and 9> 3
6*3 = 18 and 18 >3

I. 2∆2 = 0 , If ∆ is division , then the expression is invalid

II. 2∆2 = 1 , If ∆ is subtraction , then the expression is invalid
III. 4∆2 = 2 - Correct

Answer C
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Intern
Intern
avatar
B
Joined: 27 Dec 2016
Posts: 12
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 21 Aug 2017, 22:40
1
Thinking that even one criteria satisfies the condition, I have interpreted that all three options are valid

Since the question says 6∆3=<3
6/3 = 2
6-3 = 3
I applied the conditions individually for all three and opted for E.
But didn't strike that one of the option should satisfy both conditions.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15644
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 09 Jan 2018, 18:39
Hi All,

We're told that the symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division and that 6#3 <= 3. We're asked which of the three Roman Numerals must be true.

To start, let's do a bit of analysis on the inequality that we're given (and determine which math operation COULD fit this):
6#3 <= 3

6 + 3 = 9 which is NOT <= 3
6 - 3 = 3 which IS <= 3
(6)(3) = 18 which is NOT <= 3
6/3 = 2 which IS <=3

Thus, the symbol # must be either subtraction or division (although we don't know which one for sure).

I. 2#2 = 0

We've proven that the symbol is either subtraction or division, so let's see if either of those operations 'fits' this information...
2 - 2 = 0
2/2 = 1
Thus, if the symbol is subtraction, then Roman Numeral 1 IS true. However, if the symbol is division, then Roman Numeral 1 is NOT true. There's no way to know which symbol is involved though, so Roman Numeral 1 is not necessarily true.
Eliminate Answers A, D and E.

II. 2#2 = 1

With the work that we've done in Roman Numeral 1 (above), we already know that the outcome of 2#2 could be 0 or 1. This inconsistency also provides that Roman Numeral 2 is not necessarily true.
Eliminate Answer B.

There's only one answer remaining....

III. 4#2 = 2

You can still prove that Roman Numeral 3 is always true...
4 - 2 = 2
4/2 = 2
Both outcomes 'fit' the information in Fact 3, so regardless of what operation is represented, the statement IS true.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 14 Jan 2019, 10:59
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Given 6∆3≤ 3, this means ∆, can either be a "-" or a "/"
I. 2∆2 = 0, 2 - 2 = 0 But 2 / 2 != 0
II. 2∆2 = 1, 2 - 2 != 1 But 2 / 2 = 1
III. 4∆2 = 2, 4 / 2 = 2 & 4 - 2 = 2

Answer C
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 14 Jan 2019, 11:03
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


If ∆ represents + then 6∆3≤ 3 = 6 + 3 ie 9 > 3 rejected

If ∆ represents - then 6∆3≤ 3 = 6 - 3 ie 3 = 3 Accepted

If ∆ represents ÷ then 6∆3≤ 3 = 6 ÷ 3 ie 2 < 3 Accepted

Now, check the given options -

(I) 2∆2 = 0 , if ∆ represents ÷ then 2∆2 = 1 (rejected)

(II) 2∆2 = 1 , if ∆ represents - then 2∆2 = 0 (rejected)


(III) 4∆2 = 1 , if ∆ represents - then 4∆2 = 2 (Accepted) ; if ∆ represents ÷ then 4∆2 = 2 (Accepted)

Thus, Answer must be (C) Only option (III)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Manager
User avatar
G
Joined: 08 Apr 2019
Posts: 157
Location: India
GPA: 4
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 14 Jun 2019, 01:09
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Why does the question say "denotes one of the four arithmetic operations", wherein while solving, ∆ actually denotes two operations (both subtraction and division).

Coming from the makers of the GMAT itself, isn't the language a bit unclear?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15644
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 14 Jun 2019, 14:41
rishabhjain13 wrote:
AbdurRakib wrote:
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Why does the question say "denotes one of the four arithmetic operations", wherein while solving, ∆ actually denotes two operations (both subtraction and division).

Coming from the makers of the GMAT itself, isn't the language a bit unclear?


Hi rishabhjain13,

Most GMAT questions (in both the Quant and Verbal sections) require 3-5 'steps' to solve - and in many cases, at least one of the steps requires that you properly 'link' one piece of information to another and make a deduction. As a simple example, you might see a question that states A and B are integers and B > 0. The deduction here is that A can be any type of integer (negative, 0 or positive), while B can only be a positive integer. You might be thinking "why not just say that B is a positive integer?".... but that removes one of the essential elements of the question (and of the overall Exam): measuring how well you can link ideas and make deductions.

The same concept applies to this question. We start off with a broader piece of information (re: there are 4 possible math functions, but which one is it?) and then we're given a second piece of information that narrows down the possibilities (re: it's either subtraction or division, but we still don't know exact which one until we move on to the next part of the question).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
B
Joined: 24 Sep 2018
Posts: 102
Location: India
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 15 Jul 2019, 01:11
The symbol ∆ denotes one of the four arithmetic operations:addition,subtraction,multiplication,or division,If 6∆3≤ 3 ,which of the following must be true ?

I. 2∆2 = 0
II. 2∆2 = 1
III. 4∆2 = 2

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

6/3 <=3 , 6-3 <=3 same in opt 3 4/2 <=2 , 4-2<=2
Manager
Manager
avatar
G
Joined: 26 Jan 2016
Posts: 181
CAT Tests
Re: The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 17 Jul 2019, 00:30
Given:6∆3≤3

Checking for all signs

6-3=3
6/3=2
6*3=18
6+3=9
So, ∆ can be division and subtraction.

Checking the options, we get;

I.2∆2=0
2−2=0 - Correct
2/2=1 - Incorrect

II .2∆2=1

2/2=1 - Correct
2−2=0 - Incorrect

III .4∆2=24∆2=2

42=2 - Correct
4−2=2 - Correct

Hence C
Manager
Manager
avatar
S
Joined: 15 Dec 2016
Posts: 118
The symbol ∆ denotes one of the four arithmetic operations:addition,su  [#permalink]

Show Tags

New post 29 Jul 2019, 18:14
VeritasKarishma | Bunuel

As a test taker -- how are we supposed to know that ∆ should represent BOTH division AND subtraction

I assumed, the conditions applied individually (subtraction OR division) and thus opted for E

It's clear one or the other works

Since the question says 6∆3=<3
6/3 = 2
OR
6-3 = 3

--------------
GMAT Club Bot
The symbol ∆ denotes one of the four arithmetic operations:addition,su   [#permalink] 29 Jul 2019, 18:14

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

The symbol ∆ denotes one of the four arithmetic operations:addition,su

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne